Many years ago, children living in the countryside were really bored.

Grammatically correct, but I feel the word 'very' would be more appropriate here, as really seems to informal in the context of this article.

They could only have fun by themselves.

I would suggest writing it as:
They had to amuse themselves.

During summer vacations, we fellow kids had a lot of time, so we were able to take the time to catch cicadas for fun.

'We fellow kids' - you can either say 'we kids' or 'fellow kids', but not both - it is repetitive.

'So we were able to take the time' - you already stated you had a lot of time, so there is no point in writing this again.

Let me introduce you to them one by one.

The first method: fouirst find a slender bamboo pole first, then fouind horsetail hair and made itweave it into a tight-able circle, then fixedfixing the circle on the thin end of the bamboo pole.

When describing a method you will generally use the present tense, just because you don't do this anymore doesn't mean the method doesn't exist anymore.

Fouind a cicada, heold the pole, let the circle it around the cicada's head and pulled the circle back, socapturing the cicada was captured.

The second method: fouind a plastic bag and a thin piece of wire.

Used the wire to pierce through the opening of the bag, and then, fixed the wire on the thin end of the bamboo pole.

You could use it to covertrap cicadas.

The word 'cover' here is not very suitable.

The third method: fouind a little wheat flour.

Poured a the proper amount of water in it, and stirred it again and again,repeatedly until it becaome sos very sticky.

JThen, just put the sticky dough on the thin end of the pole.

It is too abrupt if you just use 'Just' at the start of the sentence, there needs to be a connection.

You could use it to stickstick it on cicadas.

Stick as a verb is pretty much exclusively used to show you stick *something on something*.

Remember: you should stick it on their wings.